Patrick Shaw (Logic and its Limits, 1997) provides a simple demonstration of how group logic often fails to follow individual logic.

Order of Preference John Mary Bill
1st…………………………… X ………… Z ……… Y
2nd………………………….. Y ………… X ……… Z
3rd…………………………… Z ………… Y ……… X

Each individual can order his or her choices: first, second, third. John, for example, prefers X to Y and prefers Y to Z; hence as an individual he logically must prefer X to Z. Likewise, Mary prefers Z to X and X to Y; so she prefers Z to Y. But the preferences of the group are not so accommodating. The reader can verify that John and Mary– a majority– prefer X to Y, so that the group as a whole prefers X to Y. A majority (John and Bill) also prefer Y to Z. But nevertheless the group prefers Z to X, because Bill and Mary prefer Z to X. It is not always possible to rank group preferences, even when individual preferences can be ranked.

This is a critical aspect of group logic for investors to understand. The activity of a stock market on a given day, quarter or year is the aggregate of the activity of the individual investors who participate in the excitement– however, the resulting moves in the market indexes is almost certainly not a reflection of the fortunes of all the individual investors, and perhaps not even the majority. The rapid rise in price of a popular ‘hot’ stock is not likely to the reflection of the opinions of the majority of market participants– and could reflect the buying action of just a handful of institutional money managers among millions of individual investors. Likewise, the fall from favor of a formerly admired business may not reflect the fundamentals of the business as assessed by the majority of investors– but could result from the heavy selling of a handful of short-sighted fund managers.

The individual parts of a larger whole simply are not one in the same. Sometimes the parts by themselves don’t even resemble the whole. One famous philosophical example is the argument that blood cannot be red. When viewed under a microscope the individual components that make up blood– white cells, red cells, and platelets– all appear a yellowish-straw color. If the parts are not red then the whole cannot be red– but by observation– blood red it is. This is called the fallacy of division– if the group is large all its members must be large too, right? Of course not. As every architect and engineer knows, thousands of triangular building blocks can be assembled into a perfectly strong and stable rectangular structure. But then, if the whole is tiny– say, an atom– then its component parts– electrons, protons and neutrons– indeed must be even tinier. Likewise, if all the parts are made of plastic then the whole must also be made of plastic. These sorts of whole/part arguments are sometimes valid, but not automatically, and should be viewed with healthy skepticism.

Consider this stock market whole/part argument:

During a protracted bull market there is a narrowing of P/E ratios due to a phenomenon commonly referred to as ‘a rising tide raises all ships’. Value investors, those who search for stocks with a PE much lower than the market average, do not thrive in a bull market as the P/E differential narrows. Therefore a value investor would much prefer a bear market environment.

The conclusion is that a value investor prefers a bear market to a bull market (as narrowing P/E ratios reduce investment appeal). The value investor would indeed suffer from scant choices if all stocks converged on a single high P/E ratio, but perhaps a great deal of narrowing could occur before that point is reached, with a great amount of profit realized along the way. No value investor wants the entire differential of P/Es to disappear, but it does not necessarily logically follow that they want no part of that difference eliminated– after all it is just this eventual narrowing that supports their investment philosophy– that stocks acquired at low P/E, if they are indeed good businesses that are simply out of favor or ignored temporarily, will one day move back toward their true intrinsic business value (i.e., rise to a higher P/E). Moving from a large P/E differential between ‘low P/E stocks’ and ‘high P/E stocks’ to complete P/E ubiquity is what mathematicians call the ‘limit of the change’. But differentials can continue to narrow for some time without equality resulting. As Patrick Shaw points out: “Cutting down on food cannot be a continuing process unless it leads to death from starvation; nevertheless, my present consumption of calories might still be too high.”

One final example from the field of economics– if one farmer increases his output he can expect to make more money. But if every farmer increases his output then it does not logically follow all of them will see rising incomes. Because of supply and demand dynamics, if a small single farmer manages to increase his output he can easily sell his extra crops into the market without upsetting prices. When all farmers suddenly increase their crop output the market will be flooded with supply, probably well in excess of demand, and prices will begin to plummet– perhaps more than wiping out the benefit of excess production for all farmers. In this case, each individual farmer hopes to have not just better absolute performance (increase crop output), but better relative performance (increased crop output relative to all other farmers).

This does not hold true in all fields. A mutual fund investor, for example, takes little solace from watching his investments fall by a smaller amount than other mutual funds– he has still lost money as the fund manager brags about good relative performance. Several years of this sort of good relative performance may wipe out his retirement savings. He cares more about absolute performance of his investment portfolio– as does every investor during a down (bear) market. Ironically, during a rising (bull) market, investors are less satisfied with an absolute return that lags behind the overall market rise– suddenly changing their emphasis to measuring positive returns relative to the market index.

This article is extracted from the WallStraits publication, The Philosophical Investor, 2005.